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2. Spencer throws a basketball out of a helicopter hoping to make a basket on the...

2. Spencer throws a basketball out of a helicopter hoping to make a basket on the ground below. He throws it with a downward velocity of 5 meters per second from a height of 100 meters. Note that the acceleration of gravity is a constant 9.8 meters per second squared (downward).

(a) Write the above information as an initial value problem for the height (position) s(t) in meters of the ball t seconds after Spencer throws it.

(b) Solve the IVP for s(t).

(c) At what time will the ball (hopefully) go through the hoop (3 m above the ground)? Round to the nearest tenth of a second.

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